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Simplifying 0.5x + 0.5x(x + -6) = 44 Reorder the terms: 0.5x + 0.5x(-6 + x) = 44 0.5x + (-6 * 0.5x + x * 0.5x) = 44 0.5x + (-3x + 0.5x2) = 44 Combine like terms: 0.5x + -3x = -2.5x -2.5x + 0.5x2 = 44 Solving -2.5x + 0.5x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + -2.5x + 0.5x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + -2.5x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -88 + -5x + x2 = 0 Move the constant term to the right: Add '88' to each side of the equation. -88 + -5x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + -5x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -5x + x2 = 0 + 88 -5x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 -5x + x2 = 88 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 88 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 88 + 6.25 Combine like terms: 88 + 6.25 = 94.25 6.25 + -5x + x2 = 94.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + -2.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + -2.5 = 9.708243919 Simplifying x + -2.5 = 9.708243919 Reorder the terms: -2.5 + x = 9.708243919 Solving -2.5 + x = 9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 9.708243919 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 9.708243919 + 2.5 x = 9.708243919 + 2.5 Combine like terms: 9.708243919 + 2.5 = 12.208243919 x = 12.208243919 Simplifying x = 12.208243919Subproblem 2
x + -2.5 = -9.708243919 Simplifying x + -2.5 = -9.708243919 Reorder the terms: -2.5 + x = -9.708243919 Solving -2.5 + x = -9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -9.708243919 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -9.708243919 + 2.5 x = -9.708243919 + 2.5 Combine like terms: -9.708243919 + 2.5 = -7.208243919 x = -7.208243919 Simplifying x = -7.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.208243919, -7.208243919}
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